find the dimensions (radius r and height h) of the cone of maximum volume that can be inscribed in a sphere of radius 2.

The Fibonacci sequence is 1, 1, 2, 3, 5,... , here each number of the sequence is the sum of the two preceding numbers in the sequence.

The Fibonacci sequence is the sequence that each number in the sequence is the sum of the preceding numbers

The first term = 1

The second term = 1

Third term will be the sum of the two preceding numbers

Third term = First term + second term

= 1 + 1

= 2

The fourth term = second term + third term

= 1 + 2

= 3

The fifth term = Fourth term + Third term

= 2 + 3

= 5

The sequence will be 1, 1, 2, 3, 5....

Therefore, the Fibonacci sequence is the sequence each number is the sum of the two preceding ones

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The required invested money is given as $2200.

Harriett Weiss earned $77 in simple interest in 6 months at an annual interest rate of 7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Here,

Applying the standard formula for the simple interest.
SI  = principal × rate × time / 100
77 =[ p × 7 × 6/12 ]/ 100
p = 77 / 7 × 2 × 100
p = 11 × 200
p = 2200

Thus, the required investment amount is specified as $2200.

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As per the exponential growth function, the cost of the same goods and services in January 1, 2013 is $291.54

Exponential growth function:

In statistics, exponential growth function mean  a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given,

The amount of goods and services that costs $200 on January 1, 1997 costs $230.16 on January 1, 2006.

Here we need to estimate the cost of the same goods and services on January 1, 2013 and also assume the cost is growing exponentially. Round your answer to the nearest cent.

Here we know that the value of

Cost on 1997 = $200

Cost on 2006 = $230.16

So, the time difference is

=> 2006 - 1997 = 6

And the amount difference is

=> $30.16

So, based on the exponential growth function, the cost of goods and services at the time of 2013 is

=> 200 + ( 1 + 30.16)⁶

=> 200 + 91.54

=> 291.54

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The ounces of butter that are needed to make a pound of jelly is  3 ounce  .

In the question ,

it is given that ,

Samuel is using 1/5 of an ounce of butter to make 1/15 of a pound of jelly.

let the number of ounces of butter needed to make a pound of jelly be "x" .

So , the equation for the situation can be represented as

( 1/5 ounce butter)/(1/15 pound jelly) = x/( 1 pound jelly)

So ,after cross multiplication ,

we get ,

15/5 = x/1

So , x = 3  .

Therefore , the ounces of butter needed is 3 ounce .

The given question is incomplete , the complete question is

Samuel used 1/5 of an ounce of butter to make 1/15 of a pound of jelly. How many ounces of butter are needed to make a pound of jelly ?

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Comparing the square root of 18 and twenty three fifths using an inequality is ✓18 < 23/5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

The square root of 18 will be 4.25

23/5 will be 4.6

Therefore, we can see that 4.6 is greater than 4.25.

In this case, ✓18 is less than 23/5.

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The percentage of students that prefer biology only is; 60%

Percentage can simply be calculated by dividing the value by the total value, and then multiplying the result by 100.

Now, we are told that 29 of the students are girls. Thus;

Number of boys = 100 - 29 = 71 boys

Now, 9 of the girls like biology. Thus, this is;

9% of the total students

20 of the boys prefer physics and this in percentage is;

20% of the total students.

27 people prefer chemistry and this is;

27% of total students

Number of boys that prefer biology = 71 - (20 + 20) = 31

Thus;

Number of students that prefer biology = 29 + 31 = 60 students

This gives a percentage of 60% of the total students.

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Answer:

55000 grams

Step-by-step explanation:

1 kg = 1000 grams  ==> kilo means 1000, so 1 kilogram = 1000 grams

Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.

55 kg* 1000 grams / 1 kg =

55 * 1000 grams / 1 =  ==> cancel out the kg

55 * 1000 = 55000 grams

The age of the bones from the skeleton of a prehistoric creature is 8460 years.

The formula to be used for the calculation of age is

ln (N/N₀) = -kt

where, N/N₀ represents represents remaining time

k is constant of proportionality

t is age or time period

The remaining time is 100 - 65 = 35

Remaining time = 35% or 0.35

Keeping the values in the above formula, we have

ln (0.35) = - 0.000124 t

-1.049 = -0.000124 t

t = 8459.67 ≈ 8460 years

Thus, the age of the prehistoric creature is 8460 years.

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Answer: 13 + 2x = 63 and the cost of one ticket is $25 (x=25)

Step-by-step explanation:

Build the equation from what it tells you.

The entire trip costs $63

The concert ticket that is included costs $13

Two passes cost the same amount, use x for what you don't know, 2x.

So,  13 + 2x = 63.

Find x = cost one pass.

13 + 2x = 63

-13.          -13

      2x= 50

    2x/2= 50/2

     x= 25

The maximum profit is maximized 70 of product A and 20 of product B are produced.

The objective function:

The profit is 50 for each product A and 60 for each product B:

P = 50A + 60B

The machine 1 constraint:

2 minutes for each product A and 3 minutes for each product B; 200 total minutes available:

2A+3B ≤  200

The machine 2 constraint:

4 minutes for each product A and 1 minute for each product B; 300 total minutes available:

4A+B ≤  300

The production constraints:

At least 8 of product A and at least 10 of product B:

A ≥  8

B ≥  10

2A+3B=200

4A+B=300

4A+6B=400

5B=100

Divide

B = 100 / 5

B=20

Also, A=70

The units are 70 and 20 respectively.

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Answer:

daymn

it's gonna be okay

The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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The distance from the point to the parametric line is given as follows:

5 units.

The first step is obtaining the vector from the line L(0, 5 + 3t, 2 + t) to the point P(5,5,2), as follows:

P - L = (5, -3t, -t).

The direction vector of the line is given as follows:

(0, 3, 1).

The dot product of the vector with the direction of the line is of zero, hence:

(5, -3t, -t)(0, 3, 1) = 0

-9t - t = 0

-10t = 0

t = 0.

Thus the point on the line which we will use to obtain the distance is of:

(0, 5 + 3(0), 2 + 0) = (0,5,2).

The the distance is obtained applying the formula for the distance between two points as follows:

Distance = square root [(5 - 0)² + (5 - 5)² + (2-2)²] = 5 units.

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Explanation:

x = number of gigabytes of data used

y = total price

Company A has the equation y = 100. The x variable is not involved since the cost is $100 no matter what.

Meanwhile, company B has the equation y = 5x+20

The slope of 5 indicates how much per gigabyte is charged. The 20 at the end is the flat fee, aka y intercept.

If we were to graph those equations, then we'd find they intersect at (16,100) as mentioned.

This means x = 16 and y = 100 pair up together.

It further tells us that both companies charge the same ($100) when x = 16 gigabytes of data are used.

This points us to choice B as the final answer.

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Answer: 227

Step-by-step explanation: (5 + 4 ) = 9                                                      

= 3 x 9^2 - 4^2

9^2 = 81

= 3 x 81 - 4^2

4^2 = 16

= 3 x 81 - 16

3 x 81 = 243

= 243 - 16

243 - 16 = 227

= 227.

Check the picture below.

Answer:

[tex]y=2^x-5[/tex]

Step-by-step explanation:

The y-intercept occurs when x = 0.

Therefore, substitute x = 0 into each equation to find its y-intercept.

[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]

Therefore, the exponential function that has a y-intercept of (0, -4) is:

[tex]\large\boxed{y=2^x-5}[/tex]

The coordinates of point B are (4, 0)

From the question, we have the following parameters that can be used in our computation:

A = (6, 10)

Midpoint = (5, 5)

The midpoint of a line from its endpoints is calculated using the following equation

Midpoint  = (x₂ + x₁)/2 + (y₂ + y₁)/2

Substitute the known values in the above equation, so, we have the following representation

(5, 5) = (6 + x₁)/2 + (10 + y₁)/2

Multiply by 2

(10, 10) = (6 + x₁) + (10 + y₁)

By comparison, we have

x + 6 = 10

y + 10 = 10

Evaluate

x = 4

y - 0

Hence, the point is (4, 0)

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The rate of change of y with respect to x for a given line is 4/5.

What is the rate of change?

The rate of change is measured by a line's slope. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.

The rate of change of y with respect to x for a given linear function is simply the slope expressed as:

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates from the graph which are:

(0, 3) and (5, 7)

Thus;

dy/dx = (7 - 3)/(5 - 0)

dy/dx = 4/5

Hence, the rate of change of y with respect to x for a given line is 4/5.

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Answer:

Step-by-step explanation:

You have triangles with two sides and the included angle given, or all three sides given. You want the measures of the missing sides or angles.

For triangle ABC, the law of cosines tells us ...

  c² = a² +b² -2ab·cos(C)

Solving for the third side, we get ...

  c = √(a² +b² -2ab·cos(C))

Solving for the angle, we get ...

  C = arccos((a² +b² -c²)/(2ab))

The names of the sides and vertices can be permuted, as long as the angle is between the given sides.

  a = √((7² +9² -2·7·9·cos(35°)) ≈ 5.176

The measure of side 'a' is about 5.2 units.

  C = arccos((8² +7² -10²)/(2·8·7)) = arccos(13/112) ≈ 83.33°

  A = arcsin((8/10)·sin(83.33°)) ≈ 52.62°

  B = arcsin((7/10)·sin(83.33°)) ≈ 44.05°

The last two angles are found using the law of sines:

  sin(A)/a = sin(B)/b = sin(C)/c

  b = √(230² +360² -2·230·360·cos(38°)) ≈ 228 . . . . feet

The third side measures 228 feet.

__

Additional comment

A calculator or spreadsheet can be programmed with the necessary formulas so that you can avoid a lot of repetitive work when you have several of these to solve. You need to make sure angles are treated appropriately, as the default is often radians, rather than degrees.

When solving for angles from three given sides, we like to solve for the largest angle first. That avoids any ambiguity when using the Law of Sines to find the other angles.

When using the Law of Sines to find a second angle after using the Law of Cosines, it can work well to find the smallest remaining angle. (In the first problem, that would be the angle opposite the side of length 7; in the last problem, that would be the angle opposite the side of length 230.)

In the picture we can see the graph represents of the function f(x)=x²-2x+3 that is curve graph.

Given that,

We have to find the graph represents the function f(x)=x²-2x+3.

We know that,

The quadratic function is f(x)=x²-2x+3.

This is a vertical parabola open downward

The vertex is a maximum

We know,

A vertical parabola's equation in vertex form is equal to

y= a(x-h)²+k

where

a is a coefficient

(h,k) is the vertex

Here

a=1

(h,k)=(0,3)  is vertex

The y-intercept is the point (0,3) is value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points is values of x when the value of y is equal to zero  

Therefore, In the picture we can see the graph represents of the function f(x)=x²-2x+3.

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complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)

results as The graph of f(2) = et te is a straight line with a y-intercept of 1.

A) f(2) = et te

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers

Step B) Find any x-intercepts:

x-intercepts: None

Step C) Find any y-intercepts:

y-intercept: f(0) = e0te = 1

Step D) Find any vertical asymptotes:

Vertical asymptotes: None

Step E) Find any horizontal asymptotes:

Horizontal asymptote: None

Step F) Find any points of inflection:

Points of inflection: None

Step G) Find any symmetry:

Symmetry: None

Step H) Sketch the graph:

The graph of f(2) = et te is a straight line with a y-intercept of 1.

B) f(x) = tan-(+)

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers except -π/2, π/

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In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .

What is a Fibonacci Sequence?

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.

so the seventh number is 3+5 = 8

8th number is 5+ 8 = 13

11th number is 21+34 = 55

now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55

Hence , the 8th number is 13 mad 11th number is 55.

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Answer:

qwqe

Step-by-step explanation:wqeqwe

The prime number that cannot be in the set is A . 2.

Prime number:

In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers

Given,

Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.

Here we know that, all prime numbers except the first prime number are odd except 2.

And here we assume that the two prime numbers are different,

So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.

Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.

There the correct option is A. 2.

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The distinction between them is that an integer is a negative number without a decimal point.

All whole numbers and negative numbers are considered integers. This means if we include negative numbers together with whole numbers, we form a set of integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers. In this article, let's learn more about integers, their definition, and their characteristics.

According to our question-

The group of integers that are neither whole nor a natural number are:

As previously noted, the third set of integers lacks a decimal point;

However, the difference between them is that; a negative number without a decimal point is referred to as an integer

From the provided set: only fit into the description of an integer, because

It does not have a decimal point

And that is unfavorable.

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The first four terms of the sequence given the sequence definition are 17, 15, 13 and 11

From the question, we have the definition of the function that can be used in our computation:

f(n) such that

f(1) = 17

f(n) = f(n - 1) - 2 if n > 1

The above definitions imply that we simply subtract 2 from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

f(2) = 17 - 2

f(2) = 15

Also, we have

f(3) = 15 - 2

f(3) = 13

Lastly, we have

f(4) = 13 - 2

f(4) = 11

Hence, the the first four terms are 17, 15, 13 and 11

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The given statement is FALSE.

Given statement;

When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure to effectively carry out and use the results.

The above-mentioned statement is FALSE.

→ We are aware that checking assumptions is crucial when applying statistics in daily life because failing to do so will prevent us from receiving fair answers to our statistical queries or drawing valid inferences. To use the good process and appropriate statistical distributions while utilizing statistics in daily life, it is crucial to examine assumptions.

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