Ten members Three juniors and seven seniors from the science club qualify for a national competition, but only five

people per school can attend the event. The coach decides to put the 10 members' names on identical slips of

paper, put the slips in a hat, and pull out five names, one at a time. Those five students will go to the national

competition. Let X represent the number of juniors selected to attend the competition.

Have the conditions for a binomial setting been met for this scenario?

Yes, all four conditions in BINS have been met.

O No, we do not know how many people overall will go to the national competition.

No, there is no way to find out the probability of choosing just one student to attend.

No, the names were pulled and not replaced in the hat, so the independence condition is not met.

Answer:

Multiplying

Step-by-step explanation:

The Multiplying of a positive integer is negative.

A taste test asks people from Texas and California which pasta they prefer brand A or brand B. The correct answer is option D.

We first give events names:

Event C: Californians were chosen for the group.

Event A: The chosen individual favors the A mark

Now note in the table that there are 275 people in total.

Then, there are 176 persons who favor the A mark.

150 persons identified as being from California.

There are 96 residents of California who favor the A brand.

Next, we have this:

[tex]P(C)= \frac{150}{275} \\P(C)= \frac{6}{11} \\P(C)=0.55\\P(A)= \frac{176}{275} \\P(A)= \frac{16}{25} \\P(C and A)= \frac{96}{275} \\P(C and A) = 0.3491[/tex]

Then:

[tex]P(CIA)= \frac{P(C and A)}{P(A)} \\P(CIA)= \frac{\frac{96}{276} }{\frac{16}{25} } \\= \frac{6}{11} = 0.55[/tex]

Two occurrences C and A are by definition independent if and only if:

[tex]P(C and A)=P(A)*P(C)[/tex]

If A and C are separate events, the following condition must be true:

[tex]P(CIA)= \frac{P(A)*P(C)}{P(A)} \\P(CIA)=P(C)\\[/tex]

Be aware that [tex]P(C)=0.55[/tex] and [tex]P(CIA)=0.55[/tex]

So:

[tex]P(CIA)=P(C)[/tex]

Consequently, the occurrences are separate, and [tex]P(C)=P(CIA)=0.55.[/tex]

To learn more about events, refer:-

https://brainly.com/question/12961938

#SPJ4

Answer:

-3.5, -3, -2 1/2, -2, 2.5

Step-by-step explanation:

Answer:

-3.5,-3,-2 1/2,-2,2.5

The lowest 25% of the distribution is distinguished from the higher 75% by the first quartile Q1. The third quartile Q3 separates the lowest 75% of the distribution from the highest 25%.

A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100. A percentage is a ratio with the second word being 100. Percentage refers to parts per hundred. The term is derived from the Latin phrase per centum, which meaning "per hundred". In mathematics, the sign% stands for percent.

Here,

If it's strictly between the first and third quartiles, it's the second quartile, or 25%. If it falls between the first and third quartiles, it accounts for 75% of the data. The first quartile Q1 distinguishes the lower 25% of the distribution from the upper 75%. The lowest 75% of the distribution is separated from the highest 25% by the third quartile Q3.

To know more about percent,

https://brainly.com/question/29172752

#SPJ4

The required money she will have at the end of the week for 10, 15, and 20 hours is $250, $375, and $500.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The equation to show how much money Mary will have at the end of the week would be:

M = 100 + (15 * h), where M is the total money Mary will have at the end of the week and h is the number of hours she works.

If Mary works 10 hours, she will have:

M = 100 + (15 * 10) = 250 dollars.

If Mary works 15 hours, she will have:

M = 100 + (15 * 15) = 375 dollars.

If Mary works 20 hours, she will have:

M = 100 + (15 * 20) = 500 dollars.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

The restaurant sold 41 ham dinners.

Let's call the number of ham dinners sold as "x".

We know that the total revenue from ham dinners is $12 * x and the total revenue from turkey dinners is $15 * 35.

So, the total revenue from both dinners is $12 * x + $15 * 35 = $1017.

We can now set up an equation:

$12 * x + $15 * 35 = $1017

Expanding the equation:

$12x + $525 = $1017

Subtracting $525 from both sides:

$12x = $1017 - $525 = $492

Dividing both sides by 12:

x = $492 / $12 = 41

So, the restaurant sold 41 ham dinners.

Answer: 13.

Step-by-step explanation:

To solve this problem, you could use an equation. (X-5)/4=2 once you solve this equation you should get 13. you should check your answer. 13-5=8. 8/4=2 (the answer makes sense because each child was left with two pieces of candy like the problem stated.

The money after 8 quarters is $4,324,500.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the amount invested in the company = $5,000,000

interest loss in each quarter = 7%

the formula for exponential decay

y = a[tex](1 - r)^{t}[/tex]

here t = time in years

1 year = 4 quarter

8quater = 2 years

t = 2

r = rate = 7% = 0.07

a = $5,000,000

y = 5,000,000(1 - 0.07)²

y = $4,324,500

Hence the amount after 8 quarters is $4,324,500.

Learn more about Exponential Function;

https://brainly.com/question/14355665

#SPJ1

Answer:

275.5

Step-by-step explanation:

In order to convert.

It is fairly simple, follow my directions and next time when you have a question similar to this you’ll know what to do!

1 kg = 2.2 lb. It is as simple as that!

So your question,

“ Convert 125 kilograms to pounds “

125x2.2 = 275 .

Our answer is very close to the verified one, so now you know how to convert kilograms to pounds!.

Learn more down below!

brainly.com/question/22192116

56.69904625 kg in 125 lbs. Likewise the question how many pound in 125 kilogram has the answer of 275.577827731 lbs in 125 kg.

125 kg*2.2046226218 lbs/1kg = 275.577827731 lbs

The weight of 125 kilograms is equivalent to 275.577827731 pounds (125kg = 275.577827731lbs). It is simple to convert 125 kg to lb. Simply use our calculator above or the method to convert 125 kg to pounds. To convert 125 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 125 kilograms to pounds is [lb] = 125 * 2.2046226218. Thus, 125 kilos is 275.577827731 pounds.

One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.

To learn more about kilograms in pounds  to refer:

https://brainly.com/question/24398277

#SPJ4

The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

To learn more about the rectangle, visit:

brainly.com/question/15019502

#SPJ4

The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

To learn more about Rectangle

brainly.com/question/15019502

#SPJ4

Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

The shop sold  [tex]9\frac{2}{3}[/tex] ounces of milk chocolate.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given  a chocolate shop sold 2 ounces of white chocolate,

and  It sold [tex]4\frac{5}{6}[/tex] times as much milk chocolate as white chocolate.

The total ounces of milk chocolate sold =  [tex]4\frac{5}{6}[/tex] x 2

29/6*2 = 29/3

The total ounces of milk chocolate sold =  [tex]9\frac{2}{3}[/tex]

Hence [tex]9\frac{2}{3}[/tex] ounces of milk chocolate is sold.

Learn more about arithmetic operations;

https://brainly.com/question/25834626

#SPJ1

The 683.67 kilowatt-hour was charged while 1640 kilowatt-hour generated the credit by not being used.

The amount of electricity consumed will be calculated by the formula -

Amount of electricity consumed = total charged amount ÷ amount of unit electricity consumed

The amount of electricity that earned the credit will be calculated by the formula -

Amount of electricity that earned the credit = total reduction amount ÷ credit on unit electricity

Keep the values in formula

Amount of electricity consumed = 82.04/0.12

Performing division on Right Hand Side of the equation

Amount of electricity consumed = 683.67

Amount of electricity that earned the credit = 4.10/0.0025

Performing division on Right Hand Side of the equation

Amount of electricity that earned the credit = 1640

Thus, the amount of electricity consumed is 683.67 units and unused electricity is 1640 units.

Learn more about electricity charges -

https://brainly.com/question/14277272

#SPJ4

The correct answer is C. 0.25 foot.

To find the depth of the mulch, we need to determine the volume of the circular mulch bed and divide it by the area. The volume of a cylinder can be calculated as:

V = πr^2h

where r is the radius and h is the height (or depth) of the cylinder.

For the circular mulch bed, the radius is 1.6 feet and we want to find the height (or depth), so we can set the volume equal to the volume of the mulch:

V = π * 1.6^2 * h

V = 2 cubic feet

Solving for h:

h = V / (π * r^2)

h = 2 / (π * 1.6^2)

Using the value of π = 3.14, we get:

h = 2 / (3.14 * 1.6^2)

h = 0.24 inches

Therefore, the depth of the mulch is approximately 0.24 inches to the nearest hundredth of an inch, which is the appropriate number of significant digits.

To convert inches to feet, divide the number of inches by 12:

0.24 inches / 12 inches/foot = 0.02 feet

Rounding to the nearest hundredth of a foot, we get 0.25 feet as the answer.

Answer: $8.30

Step-by-step explanation:

Multiply: 83 times 10. If it's in a decimal put the decimal after 8

Answer:

4q + 2

Step-by-step explanation:

4(q + 2) -6

4q + 8 -6

4q + 2

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ b=\stackrel{4+7}{11}\\ h=5.8\\ a=3 \end{cases}\implies A=\cfrac{5.8(3+11)}{2}\implies A=40.6~m^2[/tex]

==============================================

Explanation:

We have a proportion in the form:

A/B = C/D

where,

Each is measured in feet.

In this case,

Let's solve for D.

A/B = C/D

18/6 = 15/D

3 = 15/D

3D = 15

D = 15/3

D = 5

Ariadne is 5 feet tall.

By Solving the given identity equation we get A = 32/5, B = 36/5, C = 1/10 and D = -7/2.

Given  (3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = (Ax + B)/(x² + 2x + 2) + C/(x - 1) + D/(x + 1)

Taking LCM in RHS

(3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = ((Ax + B)(x² - 1) + C(x² + 2x + 2)(x + 1)+ D(x² + 2x + 2)(x - 1))/(x² + 2x + 2)(x² - 1)

3x³ + 4x² - 6x = Ax³ - Ax+ Bx² - B + C(x³ + 3x² + 4x + 2)+ D(x³ + x² -2)

3x³ + 4x² - 6x = (A + C + D)x³ + (B + 3C + D)x² +(-A + 4C)x - B + 2C -2D

Comparing coefficients of RHS with LHS

So, A + C + D = 3     --(1)

B + 3C + D = 4       --(2)

- A + 4C = -6      --(3)

- B + 2C -2D = 0       --(4)

We have 4 variables and 4 equations. Solving them, we get

A = 32/5, B = 36/5, C = 1/10 and D = -7/2

To learn more about identity equations here:

brainly.com/question/29125576

#SPJ4

Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.

As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.

Here,

Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.

To know more about function,

https://brainly.com/question/28193995

#SPJ1

The required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, cosec θ = 73/-55, sec θ = 73/-48, cot θ =48/55

Trigonometry is one of the most important branches in mathematics. The word trigonometry is formed by clubbing words 'Trigonon' and 'Metron' which means triangle and measure respectively. It is the study of the relation between the sides and angles of a right-angled triangle. It thus helps in finding the measure of unknown dimensions of a right-angled triangle using formulas and identities based on this relationship. Trigonometry basics deal with the measurement of angles and problems related to angles. There are three basic functions in trigonometry: sine, cosine, and tangent. These three basic ratios or functions can be used to derive other important trigonometric functions: cotangent, secant, and cosecant. All the important concepts covered under trigonometry are based on these functions. Hence, further, we need to learn these functions and their respective formulas at first to understand trigonometry.

Given the terminal point we know the following:

Adjacent = -48

Opposite = -55

Hypotenuse can use the Pythagorean Theorem to find:

c²=(-48)²+(-55)² = 5329

Take the square root of both sides

c=√5329 = 73

So, sin θ = -55/73

cos θ = -48/73

tan θ = 55/48

csc θ = 73/-55

sec θ = 73/-48

cot θ =48/55

Thus, the required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, csc θ = 73/-55, sec θ = 73/-48, cot θ =48/55

To learn more about trigonometry, visit brainly.com/question/29002217

#SPJ4

The area of the circle is 19.625 m²

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The radius of the circle 2.5 m

We know the area of the circle is given by

A=π×2.5²

 =3.14×6.25  where π=3.14

=19.625 m²

Hence, The area of the circle is 19.625 m²

Learn more about the area of the circle here:

https://brainly.com/question/14200825

#SPJ1

The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The radical expression is given below.

[tex]\rightarrow \sqrt[5]{32,768}[/tex]

The number 32,768 can be written as,

32,768 = 8 x 8 x 8 x 8 x 8

32,768 = 8⁵

Then the value of the expression is given as,

[tex]\rightarrow \sqrt[5]{32,768}\\\\\rightarrow \sqrt[5]{(8)^5}[/tex]

→ 8

The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

System 1 has unique solution, System 2 have infinite solutions, System 3 has no solution and System 4 have infinite solutions.

Algebra requires the simultaneous solution of two or more equations. There must be an equal number of equations and unknowns for a system to have a singular solution. The several kinds of linear equation systems are as follows:

Independent: There is just one possible outcome for the system. The graphs of the equations come together at this one location.

Inconsistent: There is no solution for the system.

1. Given these 3 equations will yield a unique solution:

x = 32, y = 5, z = -9.  

So, a unique solution exists for this

2. This is yield many solutions. It is of the form:

x = 41n + 20, y = 55n + 27, z = 10n + 4, when n can take any values.

Hence, infinite solutions exist

3. There is no answer for any of the three equations when you try to solve them.

4. Multiply the first equation by two and subtract from the third equation. Basically, the equation is the same.

Three unknowns, but no three distinct equations Thus, there are an infinite number of combinations of x, y, and z.

Hence, infinite solutions exist.

To know more about infinite solutions visit:-

brainly.com/question/27927692

#SPJ4

The solid with a semicircular base of radius "r" and cross sections perpendicular to the base and parallel to the diameter are squares is called a "right circular cylinder with a half-circle base".

The height of the cylinder is equal to the side length of the square cross sections, and the radius of the semicircular base is equal to "r". The volume of this solid can be calculated as follows:

V = (Pi * r^2 * h) / 2

where Pi is the mathematical constant pi (approx. equal to 3.14), r is the radius of the semicircular base, h is the height of the cylinder, and "/ 2" represents that the volume is half of a full cylinder with a complete circular base.

To know more about Square:

https://brainly.com/question/28776767

#SPJ4

The equation to represent the distance is, y = 20/3 *x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

they could ride 3 miles in 20 mints.

speed = 20/3

now, y is in mile the distance,

x is in mint the time

so, the equation to represent the distance is,

y = 20/3 *x.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

The total surface area of the prism is 204 cm²

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases.

Given here: A prism with triangular base with three of its faces as rectangle and its bases triangles.

Thus total surface area is the sum of areas of all these 5 faces

TSA= Sum of the area of the two slanted rectangles + Sum of the two bases + the sum of the rectangle the prism is resting on in the figure

Now dimensions of the slanted rectangles are given by length =12 and breadth =5 and the dimensions of the last rectangle are length =12 and breadth = 6

∴ TSA= 2×12×5 +1/2 ×6×4 +12×6

         = 120+12+72

        =204 cm²

Hence, The total surface area of the prism is 204 cm²

Learn more about the prism here:

https://brainly.com/question/29722724

#SPJ1

Answer:

The square root of 7 lies between the perfect squares closer to 7. Thus, √7 lies between 2 and 3.

Step-by-step explanation:

best of luck to you

The quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.

The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.

Polynomial expressions must be set equal to zero in order to find the root or zero. However, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.

The given rational expression is:

[tex]\frac{2x - 1}{x + 1}[/tex] ÷ [tex]\frac{3x^2}{x^2 + x}[/tex]

The rational expression can be written as follows:

[tex]\frac{2x - 1}{x + 1} * \frac{x^2 + x }{3x^2} \\\\\frac{2x - 1}{x + 1} * \frac{x (x+ 1) }{3x^2}\\\\\frac{2x - 1}{3x}[/tex]

Hence, the quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.

Learn more about rational expression here:

https://brainly.com/question/17134322

#SPJ1

The quadratic equation is: y= (x^2+11x+30), whose roots are -5 and -6, and whose leading coefficient is 1.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

the quadratic equation whose roots are -5 and -6, and whose leading coefficient is 1.

If the roots of the quadratic equation are "-6" and "-5", then it must have the following factors:  (x+5) & (x+6)

Therefore, we can write the equation in factor form as:

y = a (x+5) * (x+6)

where a is a real number constant factor. Now, this equation in standard form will look like:

y= a(x^2+11x+30)

Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant  factor  must be "1".

The final expression for the quadratic becomes:

y=(x^2+11x+30)

To learn more on equation click:

brainly.com/question/24169758

#SPJ1