In which month was the peak, the largest deposit, made? January June July August

So, on solving the provided question we can say that the rate of change of the volume with respect to radius = [tex]1770 = 4/3 \pi r^3S = 4 \pi r^2[/tex] [tex]dS/dt = 8 \pi r dr/dt[/tex]

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

Taking the derivative of the volume formula

[tex]DV/dt = 4\pi r*2 dr/dt\\5471 = 4 \pi r*2 dr/dt[/tex]

This equation  r and dr/dt

We can solve for r...

sphere is 1770 cubic inches

[tex]1770 = 4/3 \pi r^3S = 4 \pi r^2dS/dt = 8 \pi r dr/dt[/tex]

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Answer: P(rolling a sum of 4 or rolling a sum of 5)

Step-by-step explanation: edge2023

The scenario that uses the addition rule for mutually exclusive events is:

p(rolling a sum of 4 or rolling a sum of 5) = p(rolling a sum of 4) + p(rolling a sum of 5)

This is because the events "rolling a sum of 4" and "rolling a sum of 5" are mutually exclusive, meaning that they cannot occur at the same time. Therefore, the probability of either event occurring is the sum of their individual probabilities.

The probability of rolling a sum of 4 is 3/36, and the probability of rolling a sum of 5 is 4/36. The addition rule states that the probability of rolling a sum of 4 or 5 is the sum of their individual probabilities: 3/36 + 4/36 = 7/36

The other scenarios do not use the addition rule for mutually exclusive events:

p(rolling a sum of 4) is a single event and does not involve a second event.

p(rolling a sum of 12 or rolling a double 6) although the two events are mutually exclusive, it's not the sum of their individual probabilities.

p(rolling a sum of 11 and rolling a sum of 12) these events are not mutually exclusive, they can happen at the same time, so it's not the sum of their individual probabilities.

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An equation of the tangent line to the given curve at the specified point will be y = e(x - 1) + e.

Given the equation y = e^x /x and the point (1, e), the goal is to find an equation of the tangent line at this point.

To do this, we need to find the derivative of the equation at the point (1, e). Taking the derivative with respect to x gives us:

y' = (e^x * (1 - 1/x) - e^x/x^2) / x^2

Since we are looking for the derivative at the point (1, e), we can plug in x = 1 to get the derivative at this point:

y' = (e - e/1) / 1^2

y' = e

Therefore, the equation of the tangent line at the point (1, e) is y = e(x - 1) + e.

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This is an algebraic word problem and it evaluated to be 10 years time before the age of the man will be twice the age of the daughter.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the number of years it will be before the age of the man will be twice the age of the daughter with the letter x so that;

38 + x = 2(14 + x) {open bracket}

38 + x = 28 + 2x

38 - 28 = 2x - x {collect like terms}

10 = x

also x = 10.

Therefore, the agebraic word problem have a solution of 10 years before the age of the man will be twice the age of the daughter.

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Answer: I'm pretty sure there was suppose to be a 4th option that is not included here, none of these are correct, Lorraine can fill 8 jars.

Step-by-step explanation: First, we need to convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.

Then we divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.

⚠️Please verify inthe comments if there was indeed a 4th option⚠️

Answer:

8

Step-by-step explanation:

convert the 2.5 gallons of tomatoes to quarts. Since 1 gallon is equal to 4 quarts, 2.5 gallons is equal to 2.5 x 4 = 10 quarts.

Then divide the number of quarts by the number of quarts per jar: 10 quarts / 1.25 quarts/jar = 8 jars.

Answer: Part A. a student must find the missing length by using the Pythagorean theorem.

The answer should come out to be x=2√26 or x=−2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)

Step-by-step explanation:

Let's make x the missing length. The Pythagorean theorem says the way to set up this equation is the leg^2 + leg^2 = hypotnues^2.

Set up the problem and solve, I'll show you how to do it: x²+11²2=15²

Step 1: Simplify both sides of the equation.

x² + 121=225

Step 2: Subtract 121 from both sides.

x² + 121−121=225−121

x² = 104

Step 3: Take square root.

x = ± √104

The answer should come out to be x = 2√26 or x = −2√26 (Decimal: 10.19803902…, -10.19803902…) or (Rounded to the nearest tenth: 10.20, -10.20)

The total Number of ways to select five students out of 11 boys and 18 girls will be=104642

We have, total number of boys = 11, while the total number of girls = 18

Let us assume that,

X = total number of boys chosen

As it is given,

P(X>=4)=1

-P(X<=3)

Where, P(at most 3 boys are chosen) needs to be found out

As we know,

Here, the total number of ways to get at most 3 boys= Number of ways to get three boys and two girls + number of ways to get one boy and four girls + Number of ways to get two boys and three girls + Number of ways to get zero boys and five girls

Making the combination as per above arrangements:

We will get it as:

=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5

As we know,

The formula of combination is:

[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]

[tex]${ }_n C_r=$[/tex] number of combinations

n= total number of objects in the set

r= number of choosing objects from the set

So, applying the concept of combination in the above,

=11C3*18C2+11C1*18C4+11C2*18C3+11C0*18C5

[tex]= \frac{11!}{8! \times 3!} \times \frac{18!}{16! \times 2!}+\frac{11!}{9! \times 2!} \times \frac{18!}{15! \times 3!}+\frac{11!}{10! \times 1!} \times \frac{18!}{14! \times 4!}+\frac{11!}{11! \times 0!} \times \frac{18!}{13! \times 5!}[/tex]

[tex][\frac{11 \times 10\times9\times8! }{8!\times 6} \times \frac{18\times17\times16!}{16!\times2}]+[\frac{11\times10\times9!}{9!\times2} \times \frac{18\times17\times16\times15!}{15!\times6}]+[\frac{11\times10!}{10!} \times \frac{18\times17\times16\times15\times14!}{14!\times24}]+[\frac{1}{1} \times \frac{18\times17\times16\times15\times14\times13!}{13!\times120}][/tex]

[tex]=(165 \times153)+(55\times816)+(11\times3060)+(1\times856.8)[/tex]

=25245+44880+33660+856.8

=104641.8 = 104642 (approx)

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Answer:

48

Step-by-step explanation:

First you should subtract 43 and 19

then you get a answer 24

Multiply it by 2

you get 48

Answer:

no. of books =48 books

Step-by-step explanation:

lets say that he started with

x

books so,

(X÷2)-19=43

X÷2=24

X=48

My forecast is that you will either enter the next market or, more likely, keep your existing position. These are the theories we have.

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As per the unitary method, the expression can be used to find the average monthly cost of an x-month membership at the club is written as

(50 + 12x)/x.

The expression in math is known as the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Here we have given that Frank has to pay $50 as the registration fee and here we also given that this amount is compulsory to be paid

And we have also given that dues for $12 months is calculated as.

Then let us consider that the due to be paid every month be $x then the dues to be paid for 12 months will be 12x

Then the expression for the average monthly cost for x-month will be written as,

=> expression = total cost / total months

Then we have to apply the values on it, then it can be rewritten as,

=> (50 + 12x)/x

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There are mainly 6 methods used to solve a linear equation depending on the complexity and form of the equation.

A linear equation is represented as the equation of first order or variable having power 1 and can be written in the general form of Ax+By+C= 0, where A, B, and C are real numbers. And its simplest form is y= mx+b, where m is the slope or ratio of change in y and change in x, and b is the y-intercept. The following are the methods used to solve the linear equation:

1. Graphical Method.

2. Elimination Method.

3. Substitution Method.

4. Cross Multiplication Method.

5. Matrix Method.

6. Determinants Method

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If length of a rectangle is 4 inches shorter than its width and perimeter of  rectangle is 80 inches , then the length of rectangle is 18 in and width of rectangle is 22 in .

The Perimeter of rectangle can be calculated by using formula : [tex]2(l+w)[/tex] ;

let the width of rectangle be = w ,

it is given that the length is 4 inches shorter than width , that means ;

the width of rectangle is ⇒ [tex]w-4[/tex] ;

So , the perimeter becomes ⇒ [tex]80=2(l+w)[/tex]

⇒ [tex]80=2(w-4+w)[/tex]

⇒ [tex]40=2w-4[/tex] ;

⇒ [tex]2w=44[/tex] ;

⇒ [tex]w=22[/tex] ;

and substituting [tex]w=22[/tex] , we get [tex]l=22-4 = 18[/tex] in

Therefore , the length of rectangle is 18 in and width is 22 in .

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Answer: 6

12 divided by 2 is 6 or 6 + 6 = 12

The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double.

Circle c1 = new Circle(5);

Circle c2 = new Circle(7);

[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]

1. Create a public static method named areaSum that takes two Circle objects as parameters.

2. The method should return a double.

3. Inside the method, use the getArea() method of the Circle class to get the area of both circles.

4. Return the sum of the areas of both circles.

5. The method should look like this:

[tex]public static double areaSum(Circle c1, Circle c2){ return c1.getArea() + c2.getArea();}[/tex]

The areaSum() method takes two Circle objects as parameters and returns the sum of the areas of both circles as a double. The method uses the getArea() method of the Circle class to get the area of both circles and returns the sum of the areas.

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The type of triangle that is given by the dimensions, is a Scalene triangle.

A scalene triangle has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.

The lengths of two of the three sides in an isosceles triangle are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.

Each side of an equilateral triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.

The dimensions here are not the same which means that all the sides are not equal and so this is a scalene triangle.

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Answer: x = 23

Step-by-step explanation:

Move all terms that don't contain

x

to the right side and solve.

Hope this helps :)

The polynomial of degree 3 with the given zeros and a leading coefficient of 1 is:

P(x) = x^3 - 5x^2 - 14x

Remember to do one post per question, I will answer the first one.

We know that for a polynomial of degree N with the given N zeros:

{x₁, x₂, ..., xₙ}

We can write the polynomial as:

P(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)

Where the leading coefficient is a.

Here the degree of the polynomial is 3, and the 3 zeros are:

-2, 0, 7

And the leading coefficient is 1.

Then we can write it as:

P(x) = 1*(x + 2)*(x - 0)*(x - 7)

P(x) = (x^2 + 2x)*(x - 7)

P(x) = x^3 + 2x^2 - 7x^2 - 14x

P(x) = x^3 - 5x^2 - 14x

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The rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.

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

Here,
The recipe calls for 3 cups of ketchup for every 1/2 of mustard.
Now,
The rate in cups of ketchup per cup of mustard = ketchup/mustard
                                                                                = 3 / [1/2]
                                                                                = 3 × 2 = 6 / 1

Thus, the rate in cups of ketchup per cup of mustard is given as 6 cups of ketchup per cup of mustard.

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The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

Learn about the dimensions and components of matrices by starting your first introduction. A rectangular grid of numbers organized into rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. matrix, a collection of numbers lined up in rows and columns to create a rectangular array.  In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics. It is so named because there is just one row, and a row matrix has the order 1 n as a result.

given

Eigen values ( λ )

| A - λI | = 0

=  ( 7 - λ ) ( 11 - λ ) ( 11 - λ ) =0

= λ = 7 , 11 , 11

eigen vector for λ = 7

( A - IB ) X = 0

= Let y = 1 , n1 = ( -1  1  0 )

eigen vector for λ = 11

( A - λI ) X = 0

n2 = ( 0 1 0 ) let n3= ( -2 0 1 )

D = ( 7 0 0 ,  0 11 0 , 0 0 11 )

The real eigenvalues of the given matrix, once it has been diagonalized, are presented to its right as D = (7 0 0, 0 11 0, 0 0 11).

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According to the area of rectangle, the maximum area is given by a 300 × 500 ft rectangle that is being half of a square

The formula to calculate the area of square is written as

A = l x b

where l refers the length and b refers the breadth in rectangle.

Here we have know that if there were no river then the maximum area would be given by a square configuration since increasing the length and decreasing the width of a square by the same value t  will decrease the area by a square with sides of length t.

Here we have to add the river on one side.

As we all know that we need to fence in a rectangle on one side of the river and then here we have imagine an identical rectangle on the other side of the river.

Then the maximum area is given when the two rectangles form a square that is when we have a rectangle twice as long as wide is written as

=> 1500 feet of fence then the rectangle has fenced sides written as 500feet and 300feet.

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Answer:

h(g)x)) = - 6x + 1

Step-by-step explanation:

to find h(g(x)), substitute x = g(x) into h(x) , that is

h(g(x))

= h(2x)

= - 3(2x) + 1

= - 6x + 1

It is possible for this statement to be true for a vending machine that occasionally dispenses more or less than 6 oz of coffee per cup.

The term "on average" or "on the average" refers to the mean or expected value of a distribution. The vending machine may have some variations in the amount of coffee it dispenses, but on average it dispenses 6 oz of coffee per cup.

It is possible that the vending machine may dispense more or less than 6 oz of coffee per cup due to machine variations, incorrect calibration, or maintenance issues. However, as long as the mean or average amount of coffee dispensed over a certain period of time is 6 oz per cup, the statement is considered true.

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Answer:

C(220^2 + 420*2.5) = 800C + 200C = 1000C

Step-by-step explanation:

Let the length of the square base be L cm, and then the height of the container will be H cm. The volume of the container is given by the formula V = L^2 * H = 2000 cm3.

The cost of the top and bottom is 2C, where C is the cost per square centimeter for the sides. The cost for the top and bottom is 2 * L^2 * C. The cost for the sides is 4LH * C.

So the total cost is C(2L^2 + 4LH).

We can use the volume equation to find the height in terms of the length (H = 2000/L^2) and substitute it back into the cost equation.

C(2L^2 + 4L(2000/L^2)) = C(2L^2 + 8000/L)

To minimize the cost, we need to minimize the function 2L^2 + 8000/L, so we need to find the value of L that minimizes it.

Take the derivative of the function and make it equal to 0, then solve for L.

d/dL(2L^2 + 8000/L) = 4L - 8000/L^2 = 0

4L = 8000/L^2

L^3 = 2000

L = (2000)^(1/3) = 20

Therefore, the square base of the container should have a length of 20 cm, and the height of the container will be 2000/L^2 = 2000/20^2 = 2.5 cm.

The lowest cost would be C(220^2 + 420*2.5) = 800C + 200C = 1000C

By the Pythagorean theorem, [tex]y=\sqrt{6^2-3^2}=3\sqrt{3}[/tex].

By the geometric mean theorem, [tex]y^2=3x \implies x=9[/tex].

Answer:

4

Step-by-step explanation:

(H,H) (T,T)(T,H)(H,T)

The equation that models how many parts p each machine can manufacture in any number of minutes m is m = 1.5p

The term equation in math is defined as a mathematical sentence that has two equal sides separated by an equal sign

Here we have given that a machine manufactures a part in 11 minutes and here we have also know that a newer machine can manufacture the same part 1.5 minutes faster.

Let us consider that p refers the number of parts for old machine and m refers the time taken for manufacturing.

Then the equation can be written as,

=>  m = 1.5p

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Answer:

25:6

Step-by-step explanation:

1/0.24

100/24

50/12

25/6

The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y).

e(x+y)

e = expected

x = points earned on part 1

y = points earned on part 2

So, the expected recorded score is the total of points earned on both parts: e(x+y).

The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y). This formula is useful for quickly calculating the total score of an assignment, allowing the grade book to be updated quickly and accurately.

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The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                 4

  1                  2

  0                 0

  1                  2

  2                 4

A relation between a set of inputs having one output each is called a function.

Given that;

The input and output values of a function f (x) are shown in the table.

     X                          f (x)

     -4                           2

     -3                           1

     -2                           0

     -1                            1

     0                            2

Here, We have;

⇒ g (x) = 2f (x),

Hence, The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                2×2 = 4

  1                 1×2 = 2

  0               0×2 = 0

  1                 2×1 = 2

  2                2×2 = 4

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The graph to represent this data is pie chart.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

The graph used to represent the data is shown in the figure;

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